Differentiating adaptive Neuro-Fuzzy Inference System for accurate function derivative approximation

Authors:
Omid Khayat;Hadi Chahkandi Nejad;Fereidoon Nowshiravan Rahatabad;Mahdi Mohammad Abadi
Affiliations:
Young Researchers Club, South Tehran Branch, Islamic Azad University, Tehran 11365/4435, Iran;Birjand Branch, Islamic Azad University, Birjand, Iran;Department of Biomedical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran;Neyshabur Branch, Islamic Azad University, Neyshabur, Iran
Venue:
Neurocomputing
Year:
2013

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Abstract

Function and its partial derivative approximation based upon a set of discrete dataset are important issues in soft computing. Several function approximators have been presented most of them fits a model to the dataset so that the Mean Squared Error is minimized. In this paper, we propose to calculate the derivative of the Neuro-Fuzzy function approximator directly according to the parametric structure of the system and the available dataset. A criterion for derivative approximation is defined based on a combination of MSE and Approximate Entropy. According to this criterion, the superiority of the Neuro-Fuzzy model is demonstrated in comparison with some other types of Artificial Neural Networks and Polynomial models.